Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
Estimation of pollution sources with Physics-Informed and Bayesian Neural Networks
Submission Author:
Roberto Mamud Guedes da Silva , RJ
Co-Authors:
Roberto Mamud Guedes da Silva, Carlos Tadeu Pagani Zanini, Helio Migon, Antônio Silva Neto
Presenter: Roberto Mamud Guedes da Silva
doi://10.26678/ABCM.COBEM2023.COB2023-0789
Abstract
The use of the inverse problem approach in the identification of pollution sources in the environment has received an increasing attention in recent years. In this work, the inverse problem of identification of pollution sources location and intensity in a river is studied considering the advection-diffusion-reaction equation for the pollutant concentration, along with a Neural Network approach. In the forward problem, the location and intensity of the source term are known, as well as the other parameters present in the modelling of the phenomena involved. Additionally, because no pollutant was taken into account at the beginning, the initial condition is considered null, and the boundary conditions are set by the pollutant concentration on the boundary of the region of interest. In this way, the forward problem is solved by classical numerical methods. Such a numerical solution is then used as an input dataset for the inverse problem formulation and solution. The inverse problem is solved both by a Physics-Informed Neural Network (PINN), and by a Bayesian Neural Network (BNN). The PINN is a recent type of neural network that is trained to satisfy also the physical laws that describe the phenomena involved. However, it does not consider the possible uncertainties that are intrinsic to real world applications, making it natural to consider a Bayesian approach. In the Bayesian framework, these neural networks (PINN and BNN) serve as priors and such an approach yields a full posterior distribution of the parameters of interest. Therefore, in this work we show, with numerical examples, that the BNN can be a better option than the PINN alone, when dealing with noisy measurements. Numerical experiments related with PINN and BNN approaches are presented, demonstrating the feasibility of the strategy considered.
Keywords
Inverse problem, Physics-informed neural networks, Bayesian Neural Network
